Swing analysis method using a sweet spot trajectory

ABSTRACT

A method for analyzing sensor data from baseball swings (or swings in similar sports) that transforms data into a reference frame defined by the bat orientation and velocity at impact. The trajectory of the sweet spot of the bat is tracked through the swing, and is analyzed to generate metrics describing the swing. A two-lever model of the swing may be used to model the effects of body rotation and wrist rotation. Data may be analyzed to identify relevant events during the swing such as start of downswing, commit (wrist release), on-plane, peak bat speed, and impact. Illustrative swing metrics derived from the sweet spot trajectory, the swing plane reference frame, and the two-lever model include: forward bat speed, on-plane rotation, hinge angle at commit, hinge angle at impact, body rotation ratio, body tilt angle, and swing plane tilt angle.

This application is a continuation-in-part of U.S. Utility patentapplication Ser. No. 15/214,339 filed 19 Jul. 2016, the specification ofwhich is hereby incorporated herein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

One or more embodiments setting forth the ideas described throughoutthis disclosure pertain to the field of motion capture sensors andanalysis of motion capture data. More particularly, but not by way oflimitation, one or more aspects of the invention enable a method foranalysis of a baseball swing using data captured from a motion sensor onthe bat.

Description of the Related Art

Methods for analyzing swings of a piece of equipment, such as a golfclub, tennis racquet or baseball swings for example include videocapture systems that record high speed video of a swing and that analyzethe motion of the piece of equipment, club, racquet or bat, etc., andthe player from the video. These systems are typically expensive andcomplex, and they are not portable. Another method is to attach a motionsensor to the piece of equipment, e.g., a bat, etc., and to analyzemotion data captured by the sensor during the swing. A significantchallenge for these sensor based solutions is interpretation of thesensor data. In particular, sensors typically capture data in a localreference frame defined by the sensor geometry. This sensor referenceframe moves and rotates constantly throughout a swing. For example, fora baseball bat, this challenge is more complex since the bat hasrotational symmetry around its long axis; thus the batter can hold thebat in multiple orientations while swinging, which changes the sensordata. This applies to other sports that involve a swing of a piece ofequipment and any discussion oriented towards a bat herein is notlimiting, and can be applied to any other type of equipment thatinvolves a swing as well. There are no known methods that transformswing sensor data from a sensor based reference frame to a meaningfulreference frame that is insensitive to these changes in orientation.Existing methods emphasize vector magnitudes (such as total swing speed)in defining swing metrics because these magnitudes are invariant torotations in the sensor reference frame. However, individual componentsof sensor measurements along carefully chosen transformed axes providemore detailed and more physically meaningful information.

In baseball and related sports, the trajectory of specific point on thebat or other piece of equipment, for example the sweet spot, is ofparticular importance since this is the optimum location on the bat forstriking the ball. There are no known methods that combine analysis ofthe sweet spot trajectory with a swing plane reference frame.

For at least the limitations described above there is a need for a swinganalysis method using a sweet spot trajectory.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the invention enable a method to analyze a swing of apiece of equipment, for example a baseball bat, tennis racquet, or golfclub, etc., by transforming sensor data captured during the swing to areference frame that reflects the physics and geometry of the swingitself. This reference frame is called a swing plane reference frame.Metrics defined with respect to the swing plane reference frame providea detailed characterization of a swing; these metrics can be comparedacross swings to analyze the factors that affect swing performance. Forsimplicity, examples directed at baseball bat swings are detailedherein, however, the exemplary embodiments described herein may also beapplied to any other piece of equipment that involves a swing, includingbut not limited to a golf club, tennis racquet, etc.

One or more embodiments of the invention may obtain sensor data from asensor coupled to a bat while the bat is swung to hit or otherwisecontact a ball. The bat may be for example, without limitation, abaseball bat, a softball bat, or a cricket bat. The sensor may forexample be an inertial motion sensor that includes any or all of a threeaxis accelerometer, a three axis gyroscope, and a three axismagnetometer. The sensor may be a compound sensor that incorporatesmultiple individual sensors of any types. A compound sensor may includemultiple sensors at different locations on the bat; for example, withoutlimitation, some sensors may be located on the knob of the bat, andother sensors may be located at the tip of the bat. Sensor data may becollected throughout the swing, for example at a rate of 10 Hz, 100 Hz,1000 Hz, or more. The sensor data may be analyzed to determine the timeof impact between the bat and a ball. For example, accelerometer data,i.e., or acceleration data, may detect the shock of the impact. A battrajectory may be calculated from the sensor data. The trajectory mayinclude motion data samples at multiple points in time throughout theswing; each motion data sample may describe one or more of the bat'sposition, orientation, velocity, angular velocity, acceleration, orangular acceleration at a point in time.

Analysis of the bat trajectory may include calculating an impactvelocity vector for the velocity of the bat at the time of impact withthe ball. Using the impact velocity vector, a reference frame called theswing plane reference frame may be defined for the swing. The swingplane reference frame may be formed from three axes: a first axis may bethe longitudinal axis of the bat; a second axis may be the impactvelocity vector; and a third axis may be orthogonal to the swing planespanned by the first (bat) axis and the second (impact velocity) axis.The angular velocity vector of the bat, which is the rotational axisthat is perpendicular to the bat's instantaneous plane of rotation, mayalso be used to define or calculate one or more of the axes of the swingplane reference frame. The bat trajectory may then be transformed to theswing plane reference frame for further analysis. This analysis mayinclude creating one or more swing metrics from the transformed battrajectory.

Illustrative metrics that may be defined using the transformed battrajectory include the following: Swing plane speed at any point in timeduring the swing may be defined as an instantaneous rotational speed ofthe bat trajectory projected onto the swing plane. In one or moreembodiments, this swing plane speed may be calculated by projectingangular velocity onto the normal vector of the swing plane. Swingduration may then be calculated by defining the start of downswing asthe latest time prior to impact when the swing plane speed has magnitudezero. Subtracting the start of downswing from the time of impactgenerates a duration metric called the time to contact, which measureshow quickly the batter responds. The amount of bat motion may bemeasured as the total angle traversed by the bat both in the swing plane(yielding a metric called total swing angle) and in a plane orthogonalto the swing plane (yielding a different metric called off plane angle).A measure of bat acceleration through the swing may be defined bymeasuring the swing plane speed at the halfway point of a swing; theratio of this halfway point swing plane speed to the peak swing planespeed through the swing is defined as the swing tempo metric.

One or more embodiments may obtain a database of swings from multipleplayers. Analysis of the database may be used to generate one or moreperformance rating functions that rate swings on their relativeperformance. These performance rating functions may be applied to ratefuture swings, and to provide feedback to users on the performance andcharacteristics of their swings. Metrics and other data associated withswings in the database may be combined into feature vectors that may beused for classification and matching algorithms. For example, analysisof the database may be used to group swings into swing styles, whereswings associated with the same swing style have similar featurevectors. Feature vector clustering and matching may be used to providefeedback to a user on the style of his or her swing, and to identifyother users with similar swings. The feature vector may also includeother data related to the swing event, such as for example incomingpitch trajectory or classification, outgoing ball trajectory, or gameoutcome (such as foul, fly-out, home run, etc.) in order to refineclassification and analysis.

In situations where sensor data is unavailable or is saturated at thelimit of the sensor's range for a time interval during a swing, one ormore embodiments may extrapolate sensor data prior to or after theinterval to estimate actual values during this interval. Extrapolationmay for example use a Bezier curve. The curve may be for example a cubicBezier curve with four control points that are selected to match thevalues and the slopes of the sensor data curve at the endpoints of theinterval. One or more embodiments may use a Kalman filter, or a similarstate space estimator, to extrapolate sensor data into the timeinterval. A Kalman filter may for example incorporate a kinematic modelof the bat in order to predict motion parameters when sensor readingsare not able to fully track the motion, for example because the motionis outside the sensor's measurement range.

One or more embodiments of the invention may calculate a trajectory ofthe sweet spot or of a similar or other point on a bat or piece ofequipment, and may derive metrics describing a swing from thistrajectory. The sweet spot trajectory may be calculated from sensordata, for example from a sensor coupled to the bat, which may forexample include accelerometer or gyroscope data. Data may be transformedto a reference frame that may for example be centered at the sweet spotat the time of impact. A reference frame may be defined for example,without limitation, with a z-axis pointing vertically upward, and anx-axis oriented so that the longitudinal axis of the bat is in thexz-plane at impact. The time of impact may be calculated by searchingthe sensor data time series for event signatures that may for examplehave acceleration and angular velocity exceeding respective thresholdvalues. A sweet spot as utilized herein may also indicate a range oflocation or shape of area on the piece of equipment where an impactoccurs or is to occur, wherein the sweet spot meets a predefinedthreshold, or value, for maximum energy transfer, maximum ball speed orleast vibration or any other metric related to efficiency or power forexample, or using any other metric to define the location or range orarea or area range on the piece of equipment.

One or more embodiments may detect a virtual impact for an air swing,when a bat may not physically strike a ball. For example, one or moreembodiments may detect an air swing by determining whether the swing isa valid air swing, and then detecting a point in the swing when angularvelocity in the xy-plane is maximum. A valid air swing may for examplerequire that peak xy angular velocity and peak z-axis accelerationexceed respective threshold values.

One or more embodiments may calculate a start of downswing for a swing,and may calculate a time to contact metric as a difference between thetime of impact and the start of downswing.

One or more embodiments may calculate the trajectory of the position ofthe hands on the bat through the swing. This trajectory may be used forexample to calculate a center of rotation for the swing. For example,the center of rotation may be calculated as a point equidistant from thehand position at three different points on the hand trajectory. An axisof rotation may be calculated as an axis perpendicular to the planethrough these three points. A body tilt angle may be calculated as theangle between the axis of rotation and the vertical direction.

One or more embodiments may calculate and use a two-lever model of theswing, which models the swing mechanics as a body lever extending fromthe center of rotation to the hand position, and a bat lever thatextends from the hand position to the sweet spot. A body ratio metricmay be calculated based on the ratio of the rotation of the body leverthrough the swing to the rotation of the bat lever. The angle betweenthe bat lever and the body lever changes through the swing as the battercocks and then releases the wrist. A hinge angle may be calculatedthrough the swing based on the relative orientation between the batlever and the body lever; for example, the hinge angle may be defined asthe angle between the bat lever and the tangent to the body lever. Thehinge angle at impact may be used as a swing metric.

A commit event may be calculated to reflect when the batter releases thewrist during the swing. For example, the time of commit may becalculated as the time when the angular velocity of the hinge angleexceeds a threshold value. The hinge angle at the time of commit may beused as a swing metric. The hinge release metric may be calculated asthe difference between the hinge angle at impact and the hinge angle atcommit.

One or more embodiments may determine a swing plane for the swing. Theswing plane may be calculated based on the position, orientation, andvelocity of the bat at the time of impact. For example, the swing planemay be a plane through the sweet spot at impact, which is spanned by thebat's longitudinal axis at impact and by the velocity vector of thesweet spot at impact.

At any point in the swing, the distance between the sweet spot and theswing plane may be calculated as an off-plane distance. An on-planeevent may be calculated as the point in the swing when the off-planedistance is within a specified threshold and remains within thisthreshold until impact. An on-plane metric may be calculated as theangular range of motion of the bat or of one or both of the body and batlevers between the on-plane event and the impact event.

The bat forward velocity at any point in time may be calculated as thevelocity of the sweet spot projected onto a plane perpendicular to thelongitudinal axis of the bat. Bat speed at impact may be calculated asthe forward bat speed at the time of impact. A peak bat speed may becalculated as the maximum forward bat speed through the swing. Swingpower may be calculated as a product of the bat speed at impact, themass of the bat, and the average acceleration of the sweet spot duringthe swing.

A swing plane tilt angle metric may be calculated as the angle betweenthe bat's longitudinal axis at impact and the horizontal. An attackangle metric may be calculated as the angle between the sweet spotvelocity vector at impact and the horizontal.

One or more embodiments of the invention may include utilizing sound orat least one Virtual Reality (VR), Augmented Reality (AR) or MixedReality (MR) display, glasses or goggles to provide bio-feedback to theuser. For example, in one or more embodiments, a sound or visual displaymay be utilized to provide feedback to the user to indicate a correctposition, or movement has been achieved. This enables a user to work onportions of a swing or an entire swing using different body positions,for example to simulate different feet positions in a sand trap for agolf swing for example and obtain feedback regarding the position and/orswing using sound or visual feedback. In addition, by providing metricsregarding the body position, body movement, piece of equipment position,piece of equipment movement or any combination thereof, embodiments ofthe invention enable a user to work on developing more power andimproving skills in a bio-feedback environment and/or combineenvironment. Embodiments of the system also enable rehabilitation andgeneral training of the body based on the data gathered by the system tosuggest areas of the body to strength or stretch to improve the range ofmotion to avoid injury through use of correct biomechanics.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the ideasconveyed through this disclosure will be more apparent from thefollowing more particular description thereof, presented in conjunctionwith the following drawings wherein:

FIG. 1 shows an overview flowchart of an embodiment that processessensor data in a swing plane reference frame to generate several swingmetrics for the swing of a baseball bat.

FIG. 2 shows a reference frame based on a swing plane defined by the batorientation and by the velocity vector of the bat at the time of impactwith the ball.

FIG. 3 illustrates transformation of a bat trajectory from a localsensor frame to the swing plane reference frame of FIG. 2.

FIG. 4 illustrates various metrics derived from the swing planereference frame, including a total swing angle in the swing plane, anoff-plane swing angle, and a swing plane speed.

FIG. 5 illustrates derivation of a time to contact swing metric thatmeasures how quickly the batter responds.

FIG. 6 illustrates derivation of a swing tempo metric based on swingplane speed, which indicates how quickly the swing plane speed increasesthrough the swing.

FIG. 7 illustrates an embodiment that collects swing data from multipleusers into a swing database, and that analyzes this database to generatemethods of rating and classifying swings.

FIG. 8 illustrates an embodiment that analyzes swing tempo from multipleusers to determine a target zone for peak performance.

FIG. 9 shows an embodiment that provides feedback to a user on his orher swing by comparing the swing tempo to the target zone described inFIG. 8.

FIG. 10 illustrates an embodiment that classifies swings into swingstyles based on a feature vector that combines multiple swing metrics;feedback to a user indicates the swing style as well as identifyingother players with similar swings.

FIG. 11 shows a potential issue that may arise when a sensor has alimited range and the actual motion of the bat exceeds this measurementrange during a time interval within the swing.

FIG. 12 illustrates an embodiment that addresses the limited rangesituation shown in FIG. 11 by extrapolating sensor data from before andafter the time interval, in this example using a cubic Bézier curve.

FIG. 13 illustrates an embodiment that extrapolates sensor data using aKalman filter to estimate values when the measurement range of thesensor is exceeded.

FIG. 14 illustrates an embodiment that tracks the trajectory of thesweet spot of a bat and that calculates swing metrics from this sweetspot trajectory.

FIG. 15 illustrates a reference frame used in one or more embodiments tomeasure bat motion and to calculate swing metrics; this reference framehas the origin at the sweet spot, a vertical z-axis, and the bat is inthe xz-plane at impact.

FIG. 16 shows another view of the reference frame of FIG. 15, andillustrates several swing metrics including the bat forward velocity atimpact, the attack angle, and the swing plane tilt angle.

FIG. 17 shows a swing plane that is spanned by the bat's longitudinalaxis and the velocity of the sweet spot at impact.

FIG. 18 shows the off-plane distance between the bat sweet spot and theswing plane during the swing, and it illustrates swing metrics thatinclude the time when the bat is on-plane (within a specified thresholddistance from the swing plane), and the on-plane metric that measuresthe angular range of motion while the bat is on-plane prior to impact.

FIG. 19 illustrates an embodiment of a center of rotation calculation,which determines a point equidistant from the hand position on the batat multiple points on the swing.

FIG. 20 illustrates a two-lever model of a swing that is used tocalculate swing metrics such as a hinge angle between a bat lever and abody lever.

FIG. 21 shows a calculation of a commit event that may represent, forexample, when the wrist snaps to release the bat from a cockedorientation to complete a swing.

FIG. 22 shows an illustrative swing trajectory with several swing eventsannotated along the trajectory; it also illustrates a swing axis ofrotation and a body tilt metric derived from this axis of rotation.

FIG. 23 shows an embodiment that provides bio-feedback to the user forsetting posture or position or swing or any combination thereof viasound or AR/VR/MR visual displays, that enables working on postures,positions, swings and detecting proper or improper postures, positions,swings or portions thereof and to improve power and/or efficiency and toenable rehabilitation.

DETAILED DESCRIPTION OF THE INVENTION

A baseball swing analysis method using a sweet spot trajectory will nowbe described. In the following exemplary description numerous specificdetails are set forth in order to provide a more thorough understandingof the ideas described throughout this specification. It will beapparent, however, to an artisan of ordinary skill that embodiments ofideas described herein may be practiced without incorporating allaspects of the specific details described herein. In other instances,specific aspects well known to those of ordinary skill in the art havenot been described in detail so as not to obscure the disclosure.Readers should note that although examples of the innovative conceptsare set forth throughout this disclosure, the claims, and the full scopeof any equivalents, are what define the invention.

FIG. 1 shows an overview of an embodiment of the invention. User 101swings a baseball bat 102 to hit an incoming ball 103. Data is collectedthroughout the swing from sensor 104 attached to the bat. Sensor 104 mayincorporate any type of sensor technology or technologies to measure anyquantities, such as for example any aspects of the motion, position, ororientation of the bat. The sensor may be coupled with the proximal endof the bat, the distal end of the bat or anywhere in between. In one ormore embodiments the sensor 104 may comprise two or more sensors atdifferent locations on the bat. For example, without limitation, sensor104 may contain any or all of a three axis accelerometer 105, a threeaxis gyroscope 106, and a three axis magnetometer 107. These sensortypes are illustrative; one or more embodiments may use sensor data fromany type or types of sensors to track the swing of bat 102. In one ormore embodiments the sensor 104 may not be physically attached to thebat; for example, the sensor may be stationary and it may observe themoving bat using technologies such as video, radar, LIDAR, orultrasound. In one or more embodiments, data from multiple types ofsensors may be combined using sensor fusion. For example, sensor datafrom an inertial sensor on a bat may be fused with radar data or otherinformation from external devices to calculate a bat trajectory. Sensorsmay measure motion or other parameters on any number of axes. Sensorsmay measure these parameters at any desired frequency; highermeasurement frequency may for example support more detailed analysis ofthe swing. For example, without limitation, sensor 104 may collect dataonce per second, ten times per second, one hundred times per second, onethousand times per second, ten thousand times per second, or atfrequencies above ten thousand times per second.

In the embodiment shown in FIG. 1, bat 102 is a baseball bat. One ormore embodiments may obtain and analyze data for the swing of any typeof bat or similar object, including for example, without limitation, abaseball bat, a softball bat, a cricket bat, and in one or moreembodiments, a tennis racket, a table tennis racket, a badminton racket,a squash racket, a racquetball racket, a golf club, a polo mallet, ahockey stick, a field hockey stick, and a lacrosse stick or any othertype of equipment that involves a swing.

Data from sensor 104 is obtained in step 110. One or more embodimentsmay use any data transfer technology or technologies to obtain sensordata. For example, without limitation, data may be transferred over awireless network, over a wired network, or using a data storage mediumthat is moved from one system to another. Data may be obtained in realtime during a swing, obtained after a swing occurs, or obtained using acombination of real-time transfer and transfer after a swing event.

Steps 120 through 170 analyze data from sensor 104 to characterize theswing, resulting in swing metrics 180. These steps may be performed inany order, or in parallel. These steps may be performed on any system orcombination of systems. For example, without limitation, any or all ofthese steps may be performed on a computer, a mobile computer, a laptopcomputer, a notebook computer a desktop computer, a tablet computer, amobile phone, a smart phone, a smart watch, a microprocessor, a server,or a network of any of these devices. In one or more embodiments thesensor 104 may contain a processor or processors that perform some orall of the steps 110 through 170.

Step 120 determines the time of impact between bat 102 and ball 103.This step may for example detect a signature in the sensor data thatindicates a collision. For example, if sensor 104 includes anaccelerometer such as accelerometer 105, a rapid spike in accelerationmay be a signature of an impact. Similarly, if sensor 104 includes agyroscope such as gyroscope 106, a rapid reduction in angular velocitymay be a signature of an impact. One or more embodiments may for exampleuse sensors that directly measure impact, such as pressure sensors orcontact switches. In one or more embodiments, a swing endpoint may bedefined even if the bat does not hit the ball, for example duringpractice swings, air swings, or strikes. This swing endpoint may bebased for example, without limitation, on parameters such as thelocation of the bat relative to the plate or to an incoming ball, theaim angle of the bat, or the point in time when the bat achieves maximumvelocity or maximum angular velocity. A calculated swing endpoint may beused instead of an actual impact time for any of the subsequent metriccalculations described below.

Step 130 calculates a trajectory of the bat 102 from a starting point ofthe swing through the impact time determined in step 120. In one or moreembodiments the trajectory may also extend beyond the impact or prior tothe start of the swing. The bat trajectory may be a time series ofmotion data samples, each of which represents the state of the bat at apoint in time during the swing. For example, each sample may includedata on any or all of the bat's position, orientation, velocity, angularvelocity, acceleration, or angular acceleration. In one or moreembodiments a sample may include data for multiple locations on the bat.Methods to calculate an object's trajectory from motion sensor data areknown in the art. For example, one or more embodiments may use inertialnavigation algorithms known in the art to calculate the position andorientation of the bat over time from acceleration data (for examplefrom accelerometer 105) and from angular velocity data (for example fromgyroscope 106). Data from other sensors, such as for examplemagnetometer 107, may for example provide redundant measurements tocorrect errors in inertial navigation algorithms.

Because the orientation and position of sensor 104 changes throughoutthe swing, the bat trajectory calculated in step 130 may not be in aconvenient form for analysis. Therefore, in step 150 a standardizedreference frame is defined based on the swing itself. We refer to thisreference frame as the swing plane reference frame. In step 160 the battrajectory is transformed to this reference frame. In step 170 thetransformed trajectory is used to analyze the swing, and to generate oneor more swing metrics describing and characterizing the swing.Illustrative swing metrics 180 describe for example the timing of theswing, the speed of the swing, and the angles traversed during theswing.

FIG. 2 illustrates definition and calculating of the swing planereference frame. This reference frame is defined by the bat'sorientation and motion at the time of impact between the bat 102 and theball 103. A swing plane 212 is defined by two axes: a first axis 210 isthe longitudinal axis of the bat (along the bat's long dimension); asecond axis 211 is in the direction of the bat's velocity at the time ofimpact. The velocity vector at impact may also be calculated as atangent vector to the bat's instantaneous rotation round the angularvelocity axis. This impact velocity vector 211 may be calculated orobtained from the bat trajectory. In one or more embodiments a specificpoint on the bat, such as for example the sweet spot, may be used todefine the impact velocity vector. The swing plane 212 is the planespanned by the vectors 210 and 211. To complete the reference frame, athird orthogonal off-plane axis 213 is selected as the normal vector tothe plane 212. The swing plane 212 defined by the axes 210 and 211provides a reference frame that can be calculated from data generated bybat sensor 104. Other planes of rotation that may be relevant to thekinematics of the swing include for example the rotational plane 221 forthe batter's shoulders, and the rotational plane 222 for the batter'ships. In one or more embodiments additional sensors, for example sensorsattached to the batter's shoulders and hips, may be used to calculatethese body rotational planes in addition to the swing plane 212.

In the example shown in FIG. 2, sensor 104 has a local reference framein which sensor data is measured. This local reference frame in generalmay have a completely different orientation from the swing planereference frame defined by axes 210, 211, and 213. For example, thesensor local reference frame may have axes 201, 202, and 210; in thisexample one axis of the sensor local reference frame is aligned with thebat longitudinal axis, but the other axes are in arbitrary directionsdue to the rotational symmetry of the bat around this axis. Tofacilitate standardized analysis of swings and comparison of swingsacross players, bat trajectory information is transformed from thesensor local reference frame into the swing plane reference frame. FIG.3 illustrates this transformation. Bat trajectory 301 includes motiondata samples at various points in time, such as for example points 302,303, and 304. These samples may include any information on the state ofthe bat, such as position, orientation, or derivatives of these valueslike velocity and angular velocity. For illustration, the bat trajectory301 is shown as a single curve in three dimensional space (for exampleas a curve of bat position over time); however, in one or moreembodiments the bat trajectory may include any data with any number ofdimensions. In the sensor local reference frame defined, forillustration, by axes 201, 202, and 210, each sample point hascoordinates such as coordinates 305 for point 304. Transformation 310maps the sample points into the swing plane reference frame, for exampleusing a rotation of the axes 201, 202, and 210 into axes 210, 211, and213. For example, in the swing plane reference frame, point 304 on thebat trajectory 301 has coordinates 306.

One or more embodiments of the invention may analyze the bat trajectoryin the swing plane reference frame to measure and characterize theswing. FIG. 4 shows illustrative metrics for angular change that aredefined relative to the swing plane reference frame. Bat trajectory 401is a three dimensional curve in the three dimensional swing planereference frame 410 defined by axes 210, 211, and 213. Trajectory 401has starting point 420, representing a start of the swing, and endpoint421, representing for example the time of impact between the bat and theball. This curve may be projected onto the two-dimensional swing plane212 defined by axes 210 and 211, and various metrics may be calculatedfrom this projection. For example, the 2D curve 402 is the projection ofthe bat trajectory 401 onto plane 212. As the curve 402 proceeds fromthe starting point to the endpoint of the trajectory, it subtends anangle 403 (Δθ_(sp)) in the swing plane (with vertex at the origin). Thisangle 403, which we refer to as the total swing angle, is a swing metricthat indicates the total amount of bat movement during the swing in theswing plane. Similarly, the bat trajectory 401 may be projected onto aplane 412 orthogonal to the swing plane, and the angle 407 subtended bythe projected trajectory is a different swing metric that we refer to asthe off-plane angle. The total swing angle metric and the off-planeangle metric provide a useful characterization of how the batter ismoving the bat through the swing. Projection of the trajectory 401 ontoswing plane 212 also provides a measure of the instantaneous angularvelocity 406 of the trajectory at any point in time, such as atillustrative point 404. This instantaneous angular velocity in the swingplane, which we refer to as the swing plane speed, is a more usefulmetric of the bat's motion than for example the total linear velocity ofthe bat, which includes an off-plane component of velocity that is notas relevant for the power of the swing. The swing plane speed 406 may becalculated for example as the derivative of the instantaneous angle 405between the point 404 on the projected trajectory 402 and the axis 210.In one or more embodiments that include a gyroscope, which measuresangular velocity directly, the swing plane speed may be calculated byprojecting the measured angular velocity onto the axis orthogonal to theswing plane 212.

The curve of swing plane speed over time through the swing providesadditional useful information about the swing. FIG. 5 shows anillustrative curve 501 of the swing plane speed 406 as a function oftime. The curve typically increases through the swing as the batteraccelerates the bat. The swing plane speed reaches a maximum value 505during the swing. For some swings, the peak speed 505 may occur at thetime of impact 502; however, this is not necessarily the case for allswings. The impact swing plane speed 506 is an important swing metricsince it greatly affects the distance and power of the hit. The swingplane speed curve may be used to define an unambiguous point in time forthe start of the downswing of a swing: this start of downswing 503 maybe defined as the last point in time when the swing plane speed is zeroprior to the impact. This definition is based on an unambiguous physicalevent rather than an arbitrarily defined threshold crossing. Thisprovides a clear advantage in terms of metric consistency and physicalsignificance. If there is no zero crossing, as is the case in certainswing styles, we define the start of downswing where the slope andmagnitude of the swing plane component meet certain threshold criteria.This fallback definition does not provide the clear advantages of thezero crossing; however, because it is based on the swing planecomponent, it provides greater consistency than a definition based onvector magnitude, particularly across heterogeneous swing styles wheremuch of the variability (e.g., bat waggle) occurs in the off-planecomponent.

Using the start of downswing 503 and the time of impact 502, a totalswing time, which we refer to as the time to contact metric, may bedefined as the difference 504 between the impact time 502 and the startof downswing time 503. This time to contact metric is an importantmetric related to the batter's ability to read the pitch.

The rate at which the swing plane speed increases through the swing alsoprovides a useful metric. FIG. 6 illustrates a method to standardizethis metric by measuring the fraction of the peak speed achieved at thehalfway point of the swing. To allow meaningful comparison acrossplayers with different swing styles, the swing plane speed curve isnormalized so that swing plane speed is measured as a percentage 605 ofthe peak speed. Thus the normalized swing speed curve starts at zero atthe start of downswing, and increases to 100% at the peak speed. Ahalfway point 602 is defined for the swing, and the fraction 603 of thepeak speed at this point is defined as the swing tempo metric 604. Inone or more embodiments the halfway point may be defined as halfwaybetween the start of downswing and the time of impact. However,empirical analysis of swings shows that a more robust halfway point maybe defined by selecting a swing onset time 601 as a time at which theswing plane speed reaches a specified small fraction of the peak speed,such as for example 10%, and by defining the halfway point as halfwaybetween the swing onset time and the time of impact.

This definition of the swing tempo metric is based on the insight fromcomparing statistical distributions, where the greatest variability indeviation from an ideal curve occurs at the half-way point between twofixed endpoints. The significance of this metric comes from anunderstanding of the kinematic chain (hips, shoulders, arms, wrists) fortransferring energy from the body to a baseball bat. A rotationallyefficient swing will derive a certain amount of energy from the hips andshoulders compared to the arms and wrists. We can infer how rotationallyefficient a baseball swing is by the percentage of speed in the “body”half of the swing relative to the “arm” half. An ideal swing tempo rangeis learned from empirical data collected from elite-level batters.Deviation from the ideal tempo range, either high or low, is used toprovide feedback and prescribe drills to the batter in order to improveperformance. A low tempo typically indicates that the swing is dominatedby arms (e.g., casting), while a high tempo indicates that a swing isdominated by body (at the expense of bat control).

In one or more embodiments, additional tempo metrics may be defined atother points in a swing, in addition to the halfway point tempo metricdescribed above. For example, without limitation, an early tempo metricmay be defined as the fraction of peak speed achieved at the 25% pointof the swing, a mid-tempo metric may be defined as the fraction of peakspeed achieved at the 50% point of the swing (as discussed above), and alate tempo metric may be defined as the fraction of peak speed achievedat the 75% point of the swing. The three tempo metrics may isolate theeffect of different segments of the kinematic chain of the swing; forexample, the early tempo metric may characterize the rotation of hipsand torso, the mid-tempo metric may characterize the rotation of thetorso and arms, and the late tempo metric may characterize the rotationof the arms and bat. These percentages are illustrative; one or moreembodiments may measure swing tempo at any point or points in a swing.

In one or more embodiments, swing data and swing metrics may becollected from multiple users and organized in a swing database forfurther analysis. FIG. 7 illustrates an embodiment that collects datainto swing database 701 from multiple types of users, including forexample, without limitation, experts 702, professionals 703, amateurs704, novices 705, and instructors 706. Data in the swing database mayinclude for example, without limitation, sensor data 710, battrajectories in the swing plane frame 711, and swing metrics 712 (suchas for example the total swing angle, off-plane angle, time to contact,impact swing plane speed, and tempo metrics described above). Multiplemetrics may be combined into feature vectors 713 that may be used toclassify, categorize, compare, or analyze swings. Data from the databasemay be used for various analysis procedures 720, which may include forexample any or all of modeling swings and batters, data mining thedatabase for patterns or trends, and applying machine learningtechniques to learn relationships, functions, or categories. Outputs ofthe analyses 720 may include for example identification of bestperformances 721 that flag certain swings or groups of swings asillustrative of ideal or maximum performance; factors affectingperformance 722 that identify swing characteristics that contribute toor detract from high performance; performance rating functions 723 thatrate swings on how close they are to ideal performance levels;classifications of swing styles 724 that map swings into categoriesreflecting similar characteristics or similar performance; and matchingof swings to similar players 725 that indicate which other swings orother players are most similar to a given swing or player.

FIG. 8 illustrates an example of the data analysis methods describedwith respect to FIG. 7, using the swing tempo metric defined above.Using swing database 701 as input, data analysis and data mining process720 compares swing plane speed curves across players to determinefactors affecting performance 722. This analysis indicates that bestperformance occurs when swing tempo is in a target zone 802, for examplein a range between 804 and 803. This analysis uses normalized swingplane speed curves for the swings in database 701, with the swing planespeed axis normalized to the percentage of peak speed 605, and the timeaxis 801 normalized to a percentage of swing time between swing onset(0%) and impact 502 a (100%). The normalized swing plane speed athalfway point 602 a (50%) is the swing tempo metric for each swing.

Using the analysis illustrated in FIG. 8, an individual swing may beevaluated by comparing it to the empirically derived criteria for bestperformance. FIG. 9 illustrates an example with batter 101 generating aswing plane speed curve 901 for a swing. The measured swing tempo 902for this swing is compared to the target zone 802 in order to rate theswing's performance. Feedback is then provided to batter 101, forexample on computer screen 903. This feedback provides the swing tempometric 902, as well as a performance rating 904 that is based oncomparing the swing to performance criteria derived from empiricalanalysis. The feedback may also include specific critiques such as 905that diagnose the swing or suggest corrections or improvements.

One or more embodiments may provide feedback to a batter or to otherusers (such as a coach or trainer) using any desired method or system.For example, without limitation, feedback may be displayed on anycomputer, laptop, notebook, tablet, mobile phone, smart watch, orwearable device. Feedback may be provided using a specific app, ortransmitted via general messaging systems such as email or textmessages. Feedback may be audio, visual, haptic, or any combinationthereof.

FIG. 10 continues the example of FIG. 9 to illustrate additionalanalysis and feedback for a swing based on comparisons with swings in aswing database. In this example, a feature vector 1001 is generated fora particular swing by batter 101. For illustration, this feature vectoris a combination of the swing tempo and the impact swing plane speed.One or more embodiments may generate feature vectors using anycombinations of metrics or of any data derived from sensor data or battrajectories. Swings from swing database 701 are compared on grid 1002using this feature vector, and are analyzed (for example using clusteranalysis techniques known in the art) to categorize swings into a set ofswing styles. For example, the analysis may partition swings into threeswing styles 1004, 1005, and 1006. The feature vector 1001 correspondingto the swing by batter 101 places the swing into swing style cluster1006. Feedback to the batter indicates this swing style 1020. Inaddition, the batter's swing may be matched against typical swings fromother users to provide feedback 1021 that identifies other users withswings that resemble the batter's swing.

In some situations, one or more of the sensors that measure the motionthe bat may have insufficient range to measure the complete motionthroughout the entire swing. FIG. 11 shows an example of this situationwhere the sensor 104 on bat 102 includes accelerometer 105 with range1101, and gyroscope 106 with range 106. Taking the angular velocityaround the x-axis of the sensor as an illustrative example, the actualx-axis angular velocity 1103 exceeds the upper limit 1104 of measurementrange 1102 during time interval 1105. Therefore, the measured sensorvalues 1106 cannot track the true values 1103 of the motion during thisinterval 1105. Instead the measured value 1107 during this interval issaturated at the upper limit 1104. This saturation may affect theaccuracy of swing metrics. This example using the x-axis of thegyroscope is illustrative; a similar issue may occur with any sensor(including for example the accelerometer 105 as well as the gyroscope106) and with data from any axis of any sensor.

To address this issue, one or more embodiments of the invention mayextrapolate sensor data from prior to or after the time interval 1105when the sensor is saturated. Extrapolation may also be used when sensordata is unavailable for a period of time for any other reason, forexample because of a limited sampling rate, a recalibration period, or adefective sensor. Extrapolation may be used for any sensor or sensors,or any axis of any sensor or sensors. Embodiments may use any method toextrapolate sensor data into any time interval. FIG. 12 illustrates anembodiment that extrapolates sensor data from both endpoints of the timeinterval by constructing a Bezier curve 1200 for the values in theinterval. In this example, the curve 1200 is a cubic Bezier curvedefined by the four control points 1201, 1202, 1203, and 1204. This isillustrative; one or more embodiments may use Bezier curves or any othersplines or curves of any order. Control points 1201 and 1204 match thevalues of the sensor measurements 1104 at the endpoints of interval1105. The internal control points 1202 and 1203 are chosen to match theslopes of curve 1104 at these endpoints. Specifically, the tangent value1205 of the curve 1104 at point 1201 is the slope of the line betweencontrol points 1201 and 1202, and the tangent value 1206 of the curve1104 at point 1204 is the slope of the line between control points 1203and 1204. Points 1202 and 1203 may also be chosen to limit for examplethe maximum value of the curve 1200 in the interval.

One or more embodiments may select control points for a Bezier curve insuch a way as to satisfy the initial and/or final conditions (magnitudeand slope) and also to satisfy additional constraints on the maximumabsolute value and maximum extrapolation duration. For two-sidedextrapolation (no impact events), four control points may be used asshown for example in FIG. 12: the initial and final points are placedwhere the curve crosses the saturation threshold, and two interiorcontrol points are along a line matching the slope of the curve at somedistance, which is constrained by some maximum time duration and by amaximum absolute value. This approach provides control of the shape ofthe extrapolation curve better than a cubic polynomial fit, which willmatch the same slope and value constraints but may exceed the otherphysical constraints. If the initial or final edge of the saturationinterval is an impact event, then the unconstrained edge may berepresented by a single control point, resulting in a three-point Beziercurve. Again, the time and value for this single control point may beselected to achieve the desired shape of the extrapolated curve into theimpact event. Because a Bezier curve is not parametric in time, it maybe necessary to resample the extrapolated curve at the original sampletimes. This type of Bezier extrapolation may be applied to an individualsaturated sensor axis (independent of the other components) or acomposite value (e.g., the x-y resultant or total vector magnitude). Theshape of the composite curve may be easier to model or constrain thanthe underlying individual components for particular kinematic events,resulting in increased accuracy of the extrapolated result. If theunderlying component values are needed, they can be obtained by solvingfor the unknown saturated component(s) from the extrapolated compositeresult and unsaturated component values (the result will beunder-determined if more than one component is saturated).

Another approach to extrapolation that may be used in one or moreembodiments is to use a Kalman filter (or a variation of a Kalman filterlike an Extended Kalman Filter or an Unscented Kalman Filter). FIG. 13illustrates an example that uses this approach. Kalman filter 1301incorporates a kinematic model 1302 of the bat 102. The system state1303 is estimated for each sample point, and this estimate is correctedbased on measurements 1304. The state 1303 for example may include theposition r(t) and the orientation Q(t) of the bat, and the measurements1304 may include for example accelerometer values a_(x), a_(y), a_(z)and gyroscope values ω_(x), ω_(y), ω_(z). During time intervals when oneor more measurements are not available or are saturated, such as x-axisangular velocity 1306 during time interval 1105, the filter 1301continues to predict state values 1303. Therefore, the curve 1104 can beextrapolated to curve 1308 through interval 1105; for example, theorientation 1307 may be differentiated to estimate the x-axis angularvelocity 1308 in this interval.

In general, one or more embodiments may use a recursive state spaceestimator (e.g., Kalman filter) with a kinematic model of the physicalbody or equipment being measured. The state-space propagation model maybe used to impose appropriate physical constraints. The state spaceestimate and its uncertainty (covariance) may be updated using thenon-saturated measurements from the various sensors. An estimate of themissing (saturated) parameter may then be derived from the state spaceestimate. Likewise, the uncertainty in the estimated parameter may bederived from the model uncertainty. Either the state space propagationmodel or the measurement model (or both) may be non-linear, in whichcase a linearized (EKF) or sigma-point (UKF) filter may be used.Finally, the uncertainty in the extrapolated time series (or the statespace estimate itself) may be propagated to derived metrics. Forexample, in a baseball swing like the swing illustrated in FIG. 13, thegyroscope may be saturated into impact, which affects the accuracy ofthe swing speed measurement. Using this approach, it is possible toestimate the actual swing speed and provide an uncertainty interval(error bars).

In one or more embodiments, a swing of a bat or similar equipment may bedecomposed into key events and metrics that provide insight into overallswing quality. Some of these events and metrics may be related to orderived from the trajectory of a sweet spot of the bat. FIG. 14 shows anillustrative swing of bat 102 by batter 101. The bat is equipped with asensor 104, which may for example include a motion sensor with anaccelerometer and a gyroscope. One or more embodiments may obtain sensordata from sensor or sensors 104, and may use this sensor data tocalculate the trajectory 1402 over time of sweet spot 1401 of the batthrough all or a portion of the swing. The sweet spot location on a batmay be determined by any desired method. For example, several commondefinitions for the sweet spot of the bat are that it produces themaximum energy transfer to the ball, that it produces the maximum battedball speed, or that it results in the least vibrational sensation(sting) in the player's hands. These results are not always produced bythe same spot on a bat. In addition, the spot may vary based on bat type(wood or aluminum), weight, shape, and other factors. For a morein-depth discussion of the definition, size, and location of the sweetspot for different bat types, see for example Daniel A. Russel, “Physicsand Acoustics of Baseball and Softball Bats.”

In one or more embodiments, an illustrative definition of a sweet spotmay be a location somewhere between four and eight inches from the tipof the bat, such as for example a single point on the centerline of thebat six inches from the tip.

In one or more embodiments, data from sensor 104 may be integrated orotherwise analyzed to estimate the sensor velocity and position in aninertial (world) coordinate frame. The known position of the sweet spotrelative to the sensor may then be used to calculate the sweet spottrajectory 1402 in this reference frame. In one or more embodiments, theworld reference frame may be defined as illustrated in FIG. 15, whichshows the bat at the point of impact with a ball (or at another point intime defined as a real or virtual time of impact). The origin of thereference frame is at the sweet spot of the bat 1401 at the moment ofimpact. Gravity is in the −z direction; hence the z axis 1513 pointsvertically upward. The world coordinate system is not based on anabsolute horizontal reference point such as home plate or absolutenorth. Instead, the world frame is rotated so that the bat longitudinalaxis 1501 is in the xz plane pointing in the +x direction 1511 (forright handed batters) or −x direction (for left-handed batters). Theforward velocity of the bat is in the yz plane pointing in the +ydirection 1512. Because of this definition, the actual orientation ofthe world coordinate frame will vary from swing to swing.

FIG. 16 shows a close-up view of the reference frame illustrated in FIG.15, shown again at the point of impact of the swing. The reference frameorigin is the location 1401 of the sweet spot of the bat at impact. The−z axis 1513 a is in the direction of gravity, pointing verticallydownward. Bat longitudinal axis 1501 is in the plane defined by the xaxis 1511 and the −z axis 1513 a. The y-axis 1512 is perpendicular tothe x-axis and to the z-axis. In general, the bat may not behorizontally level at the time of impact; instead there may be a nonzeroangle 1603 between the bat axis 1501 and the (horizontal) x-axis 1511,which is referred to as the vertical bat angle. Vertical bat angle isdefined as the vertical direction of the bat with respect to horizontalat impact. Vertical bat angle is negative below horizontal and positiveabove horizontal. The swing plane tilt angle 1603 is the vertical batangle at the moment of impact. The swing plane tilt angle is usuallynegative, meaning the bat is pointing toward the ground. A level batwould result in a swing plane tilt angle of 0°. Swing plane tilt angleis important for understanding adjustability and correlations to pitchtypes and locations. Pitch location will determine changes in the batangle at impact. Adjusting the swing plane tilt angle to meet the pitchshould be done early in the swing in order to achieve maximumefficiency. Adjustment later in the swing drains energy from the speedof the bat. The swing plane tilt angle should match the location of thepitch. Steeper angles are required for low, inside pitches, andshallower angles are required for high, outside pitches.

The velocity of the bat at impact may also in general not be horizontal;the attack angle 1602 is the angle of the bat's forward velocity atimpact 1601 with respect to the horizontal y-axis 1512. Attack angle isnegative below horizontal and positive above horizontal. A positivevalue indicates swinging up, and a negative value indicates swingingdown, where zero is perfectly level. Attack angle is important for tworeasons: First, matching the bat path to the pitch path increases thelikelihood of contact. Because the pitch is thrown from an elevatedmound, it is typically on a downward angle as it crosses the plate.Therefore, a positive attack angle provides more opportunity to executeagainst a variety of pitches, which vary in height, speed, and angle.Second, a positive attack angle will usually maximize launch distance,increasing the scoring value of the at-bat. The average fastball crossesthe plate at a 6° downward angle, while an average breaking ball crossesthe plate at 10°. Other factors include swing speed and style, pitchvelocity and location, and game situation. Given the variation inincoming pitch descent angles and desired launch angle, the optimalattack angle is usually between +2° to +14° degrees. In a real gamescenario, adaptation may be required to put the ball in play. The idealattack angle results in the maximum distance for a given bat speed. Forslow bat speeds, the ideal attack angle is around 21°, and it getssmaller with increasing speed. Discussions of ideal launch angle, exitspeed, and scoring value appear for example in Nathan, “Optimizing theSwing,” at www.hardballtimes.com/optimizing-the-swing, and in Arthur,“The New Science of Hitting,” atwww.fivethirtyeight.com/features/the-new-science-of-hitting.

The bat forward velocity 1601 is the projection of the velocity vectorof the sweet spot onto the plane perpendicular to the bat longitudinalaxis 1501; it ignores any speed in the direction of the bat axis 1501.

FIG. 17 illustrates a definition of a swing plane from which variousswing metrics may be derived. Swing plane 1701 may for example bedefined as a plane through the sweet spot 1401 which is spanned by thebat longitudinal axis 1501 at impact and by the bat forward velocity1601 at impact. This swing plane is oriented so that it contains boththe length of the bat and bat velocity at the moment of impact. Theswing plane normal vector may found by normalizing the cross product ofthe bat length and bat velocity vectors. The normal vector is centeredat the sweet spot of the bat at the moment of impact, i.e., at (0, 0,0).

A swing may be analyzed for example by decomposing the motion into swingplane versus off-plane components. Off-plane motion may for example becharacterized by the distance of the sweet spot of the bat from theswing plane at any moment in time. FIG. 18 illustrates this distance ofthe sweet spot 1401 to the swing plane 1701 at several points in a swingprior to impact. For example, at the position of the bat shown in thefigure, the off-plane distance is 1801. As the swing progresses towardsimpact, the sweet spot approaches more closely to the swing plane 1701.When the distance reaches a specified threshold 1802, the swing isconsidered “on-plane” at that moment (provided that it remains at orbelow this distance from that moment until impact). For example, thethreshold may be set to 3 inches.

Based on the distance between the sweet spot and the swing plane, anon-plane metric may be defined as the total angular range of motion (forexample in degrees) of the swing where the sweet spot of the bat iswithin the threshold value (such as three inches) from the swing plane.For example in FIG. 18 the on-plane metric is the angle 1805 between theray 1803 at the on-plane event and the ray 1804 at the impact event.This metric measures an aspect of the quality of the swing because theplayer typically wants the energy from the body and arms to increaseforward bat speed rather than change its direction. Changing batdirection takes more energy as bat speed increases, so an efficientswing gets on plane early and stays on plane as it approaches impact.Ideally, a batter will read the pitch early and adjust the entire bodyto align the swing plane with the pitch location. This enables maximumbat speed for every pitch type. In one or more embodiments, the systemmay report the percentage of total velocity that is generated while thebat in on plane. For example, if the velocity is 40% of the peak whenthe bat gets on plane, then the “on plane” metric is 60%.

One or more embodiments may analyze the motion of a position on the batwhere the hands grip the bat, in addition to or instead of analyzing themotion of the bat sweet spot. FIG. 19 illustrates an embodiment thatdetermines a center of rotation 1903 for a swing by determining theposition of the hands at three points in the swing, at location 1902 a,1902 b, and 1902 c. The center of rotation is selected for example asthe point 1903 that is equidistant from these three points. One or moreembodiments may use any point or points on hands trajectory 1901 todetermine one or more centers of rotation for the swing. For example,point 1902 a may be selected as the time when the xy magnitude of thegyroscope value from the sensor is at 50% of its impact value; point1902 b may be selected as the time when the xy magnitude of thegyroscope value is at 80% of its impact value; and point 1902 c may beselected as the impact time. Using the hand positions at these times,the center of rotation may be calculated using the formula for thecircumcenter of a triangle defined for example inen.wikipedia.org/wiki/Circumscribed circle.

Three points on hands trajectory 1901 also define a plane, and thereforedefine an axis of rotation through the center of rotation 1903 that isperpendicular to that plane. The orientation of this axis of rotationmay also be used in one or more embodiments as a metric describing theswing. The three points that define the center of rotation lie in aplane that is typically tilted downward in front of the body. The axisof rotation may be calculated for example using the cross product of anytwo of the radius vectors from the center of rotation calculation.

In one or more embodiments, a two-lever model may be used to describeand analyze a swing. During the early part of the downswing, anexperienced batter rotates the core, arms, and bat as a single,connected unit. Then the batter commits by snapping the wrist, whichmoves the tip of the bat away from the body. The elbow may also extend,depending on ball location. This optimal kinematic sequence results inmaximum speed and control.

The kinematic chain includes core, shoulder, elbow, and wrist rotation.In some situations, it may not be feasible to measure all thesemovements directly using, for example, a single inertial sensor on thebat. Instead, one or more embodiments may use a simplified two-levermechanical model to distinguish “body” rotation from “bat” rotation. Thebody contribution ends at the hands. It measures rotation around thebody center of rotation, which is primarily core, shoulder, and someelbow extension. The bat component measures motion around the handposition, which is primarily due to elbow and wrist rotation. In aconnected swing, the shoulder and elbow contributions are small, and thebody component of our model closely approximates core body rotation.

FIG. 20 illustrates a swing model that employs a simple two-levermechanical system. This model focuses on the swing-plane and ignores anyoff-plane motion, which is characterized independently. The body leveris hinged at the body center of rotation and ends at the hand position.The bat lever is hinged at the hand position and extends along the axisof the bat. This model is illustrated in FIG. 20. Body lever 2001extends from center of rotation 1903 to hand position 1902, and batlever 2002 extends from hand position 1902 to sweet spot 1401.

Total bat speed is a combination of body rotation and bat rotation. Thebody ratio may be calculated the percentage of total rotation that isattributed to the body. An efficient swing uses both the body, arms, andwrists in the appropriate kinematic sequence. A swing that is mainlybody rotation or mainly arm rotation is not as powerful as a swing thatuses the entire kinematic chain. The body should contribute about 40% to50% of the total rotational speed. There may be some variation due toindividual style, but a value that is consistently outside this rangeusually indicates a poor kinematic sequence.

As the bat moves through the swing, the angle between the bat lever andthe body lever changes. An angle that reflects the relative orientationof the bat lever and the body lever is called the hinge angle. In theillustrative embodiment shown in FIG. 20, the hinge angle 2004 is theangle between the bat lever 2002 and the tangent 2003 that isperpendicular to the body lever 2001 in the two-lever mechanical model.Hinge angle is negative when the tip of the bat is angled toward thebody and positive when the tip is angled away from the body.

One or more embodiments may incorporate a method of calculating a commitevent. The commit event, also known as wrist release, occurs when thehinge angle is “released”. In other words, the moment when the hingeangle starts to move in a positive direction away from the body. Commitis the transition point in the kinematic chain between body-only motionand the wrist snap contribution. A batter begins the swing with the batangled towards the body. At commit, this hinge angle is released and thewrist is snapped forward to add speed to the bat and to contact theball.

FIG. 21 illustrates a method of calculating a commit event that may beused in one or more embodiments. The hinge angular velocity 2102 may befound by taking the first derivative of the hinge angle time series2101. Any desired method may be used to calculate or estimate aderivative; for example, one or more embodiments may use a centered,five-sample window to reduce sample noise. The commit event 2104 may bedefined as the instant when the hinge angular velocity 2102 exceeds athreshold value 2103 prior to impact. For example, a threshold value of60 rpm (360 dps) is illustrated in FIG. 21.

One or more embodiments may define a sequence of events through a swing,and may derive one or more metrics from these events. FIG. 22 shows anillustrative swing with events annotated at the point in the swing whenthey occur. Event 2201 is the start of the downswing of the swing. Startof downswing indicates the start of significant motion of the downswing.An illustrative algorithm that may be used in one or more embodiments tocalculate the start of downswing is as follows. Start of downswing iscalculated by looking at the gyro xy resultant time series. Startingfrom the peak value, work backwards one sample at a time. For eachsample, fit a straight line through the peak value and the sample ofinterest. Find the moment in time where this straight-line approximationcrosses through zero angular velocity. This is an estimate of the startof downswing. Repeat this for every sample until the angular velocity ofthe sample of interest is less than 10% of the peak value. Keep thelatest start of downswing estimate that was found during this search.This start of downswing algorithm uses the xy resultant, which is abetter proxy for overall bat motion than, for example, using only the ycomponent of motion. The model-based algorithm also provides moreconsistent estimates than a threshold-based or zero-crossing algorithm.By fitting a model to the overall shape of the angular velocity curve,the algorithm ignores meaningless hand motion near the start ofdownswing, where the signal is on the same order of magnitude as thenoise. In one or more embodiments, the angular velocity curve isdecomposed into two additive components, body lever and bat lever, and ametric is derived therefrom and optionally reported to the user and/orutilized for internal calculations. In some embodiments, other metricsmay also be reported including measuring and comparing two parts (bodyand bat rotation) and utilizing peak speed ratios, amount of rotationratios, peak angular velocity ratios, centripetal acceleration, i.e.,how quickly a user starts accelerating a bat through body rotation toform metrics. Another metric may be formed by dividing peak hand speedby peak bat speed or an average of the hand speed and bat speed fromcommit to impact to reduce variability in the measurement. In one ormore embodiments, any of these metrics or any other metrics definedherein may be provided to the user through sound, for example if over,equal to, or under a predetermined threshold, or via a visual display,or AR/VR/MR display (or through both audio and visual) to provide theuser with biofeedback for use by the user to observe and/or alterposition, posture, swing.

Commit event 2014, also known as wrist release, occurs when the hingeangle is released, as described with respect to FIG. 21.

The on-plane event 1803 occurs when the sweet spot approaches to withina threshold (such as three inches, for example) of the swing plane, asdescribed with respect to FIG. 18.

For a swing that hits a ball, impact event 1804 occurs when the bat hitsthe ball and when this impact is detected by the sensor or sensors. Oneor more embodiments may also detect a virtual impact event even when thebat does not hit a ball (for example, for an “air swing”), as describedbelow.

For embodiments with an accelerometer, a simple impact detection may beperformed by searching for a large discontinuity in accelerometerreadings, corresponding to the shock of the impact. However, certainbatters generate accelerometer noise greater than 4 g prior to trueimpact. This has been observed in internal testing and in pro-levelswings. Analysis shows that this noise is almost always associated withhigh bat roll (z-axis angular velocity). Presumably, the bat is slippingin the grip, and the noise is caused by friction of the bat against thehands or gloves. Therefore, in one or more embodiments, the impactdetection algorithm may use both the gyro and accelerometer to detectimpact. The gyro search detects impact energy that is spread out overone or more subsequent samples. Searching forward, keep a running sum ofthe maximum gyro x, y, or z discontinuity. Reset the sum to zero if thediscontinuity drops below 540 dps and remember that sample. Stopsearching if the total discontinuity exceeds 1040 dps. The gyro-onlyimpact is the last sample that was remembered.

Starting from the gyro-only impact sample, search backward until theaccelerometer x, y, or z discontinuity is less than a threshold (80% ofthe saturation value). Usually, this occurs zero or one samples prior tothe gyro-only impact, but sometimes it can more. Impact is defined asthe sample just before the accelerometer discontinuity.

In rare cases, there is insufficient energy in the gyro signal to detectimpact. In this case, impact is the defined as the sample just beforethe first accelerometer discontinuity that exceeds the threshold.

In one or more embodiments, air swings are supported by enabling an airswing version of the impact detection algorithm. If the system does notdetect an impact event, the baseball swing processor determines whetherthe swing is a valid air swing. The air swing detection algorithm mayfor example look for peaks in the gyro xy resultant and accelerometer zcomponent. A swing may be classified as a valid air swing if forexample: the gyro xy peak exceeds 500 dps; the accelerometer z componentpeak exceeds 4 g; and the two peaks occur within 100 ms. In the case ofa valid air swing, the time of the gyro xy peak may be used as a proxyfor the impact event in all subsequent calculations. Processing of airswings continues the same as for impact swings. All swings may beconsidered invalid if the air swing criteria are not met, even if thereis a valid impact signature.

Peak bat speed event 2202 occurs at the moment of maximum forward batspeed, which happens at or before the moment of impact. Peak bat speedis calculated using the forward bat speed time series. Working backwardsfrom impact, peak bat speed is located by finding the sample with thepeak value.

Average power generated during the swing may be calculated aspower=mass×speed×acceleration, where mass is the effective mass of thebat, speed is the bat speed at impact, and acceleration is the averageacceleration during the downswing (bat speed/time to contact). Power maybe measured in Watts. The more mass the batter accelerates to highspeed, the higher the power.

Based on the start of downswing event 2201 and the impact event 1804, atime to contact metric may be calculated as the elapsed time betweenstart of downswing and impact. The clock starts when there is sufficientdownswing motion and ends when the bat contacts the ball (or at acorresponding virtual impact event for an air swing). Time to contactmeasures the total time it takes to complete a swing. A major leaguefastball takes about 400 milliseconds from pitcher to home plate. Inthat time, the batter must recognize the pitch, decide whether tocommit, and execute the swing. The quicker the time to contact, the moretime the batter has to recognize and commit to good pitches. The idealtime to contact depends on age, strength, bat length and weight,experience level, and swing style. Our testing shows the typical time tocontact for different age groups and skill levels: Little League:230-400 milliseconds; Senior League: 185-325 milliseconds; High School:140-260 milliseconds; College/Pro: 100-200 milliseconds.

FIG. 22 also illustrates metrics related to the orientation of theswing. For example, axis of rotation 2204, which is perpendicular toplane 2203 spanning points on the hand trajectory and is through centerof rotation 1903, forms a body tilt angle 2205 with the vertical axis.The center of rotation is a point at the center of the arc traced by thehands and is usually near the body's center of rotation. The axis ofrotation is the axis that the body rotates around and is usually alignedwith the spine. The body tilt angle is the angle between the axis ofrotation and vertical. The body and bat should rotate around the sameaxis. A large difference between the swing plane tilt angle and the bodytilt angle is an indication of a disconnected swing. In an efficientswing, the swing plane tilt angle and body tilt angle should beclosely-aligned.

FIG. 23 shows an embodiment that provides bio-feedback to the user forsetting posture or position or swing or any combination thereof viasound or AR/VR/MR visual displays, that enables working on postures,positions, swings and detecting proper or improper postures, positions,swings or portions thereof and to improve power and/or efficiency and toenable rehabilitation. One or more embodiments of the invention mayinclude utilizing sound, e.g., via headphones 2302, or at least oneVirtual Reality (VR), Augmented Reality (AR) or Mixed Reality (MR)display, glasses or goggles 2301 to provide bio-feedback to the user. Inone or more embodiments the audio and/or image components 2301 and/or2302 may be coupled with or formed into a helmet, such as a batter'shelmet for example. This enables the user to see the pitch approach,wherein the headset tracks the ball coming to provide metrics, and afterthe ball is hit, the system provides the user with the hitting metricsand/or a 3D tracer overlay, for example of the swing. MR is alsoreferred to as “hybrid reality” and includes use of real and virtualdata to produce novel environments and visual displays that include realand computed objects and interact, which also may include real-timedisplay of data. For example, in one or more embodiments, a sound orvisual display may be utilized to provide feedback to the user toindicate a correct position, or movement has been achieved. This enablesa user to work on portions of a swing or an entire swing using differentbody positions, for example to simulate different feet positions in asand trap for a golf swing for example and obtain feedback regarding theposition and/or swing using sound or visual feedback. In addition, byproviding metrics regarding the body position, body movement, piece ofequipment position, piece of equipment movement or any combinationthereof, embodiments of the invention enable a user to work ondeveloping more power and improving skills in a bio-feedback environmentand/or combine environment. Embodiments of the system also enablerehabilitation and general training of the body based on the datagathered by the system to suggest areas of the body to strength orstretch to improve the range of motion to avoid injury through use ofcorrect biomechanics.

While the ideas herein disclosed has been described by means of specificembodiments and applications thereof, numerous modifications andvariations could be made thereto by those skilled in the art withoutdeparting from the scope of the invention set forth in the claims.

What is claimed is:
 1. A swing analysis method using a sweet spottrajectory, comprising: obtaining a time series of sensor data from asensor coupled to a piece of equipment during a swing of said piece ofequipment, wherein said sensor comprises a three-axis accelerometer thatgenerates acceleration data; and, a three-axis gyroscope that generatesangular velocity data; determining a time of impact of said swing;obtaining a location of a sweet spot of said piece of equipment;defining a reference frame; calculating a trajectory of said sweet spotrelative to said reference frame based on said sensor data; and,calculating one or more swing metrics based on said trajectory of saidsweet spot and on said time of impact.
 2. The method of claim 1 whereinsaid piece of equipment comprises a bat.
 3. The method of claim 1wherein said reference frame comprises an origin at a position of saidsweet spot at said time of impact; a z-axis pointing vertically upwardfrom said origin in a direction opposite to a gravity vector; an x-axisperpendicular to said z-axis and oriented so that a longitudinal axis ofsaid piece of equipment lies in a plane defined by said z-axis and saidx-axis at said time of impact; and, a y-axis perpendicular to saidx-axis and to said z-axis.
 4. The method of claim 1 wherein saidcalculating said time of impact comprises searching said time series ofsaid sensor data for a change in said angular velocity data exceeding afirst threshold; and, searching said time series of said sensor data fora change in said acceleration data exceeding a second threshold.
 5. Themethod of claim 3 wherein said calculating said time of impact comprisesdetermining whether said swing is a valid air swing; and, when saidswing is said valid air swing, setting said time of impact to a timewhen a magnitude of said angular velocity data projected onto anxy-plane defined by said x-axis and said y-axis in said reference frameequals a peak value of said magnitude of said angular velocity dataprojected onto said xy-plane during said swing.
 6. The method of claim 5wherein said determining whether said swing is said valid air swingcomprises determining whether said peak value of said magnitude of saidangular velocity data projected onto said xy-plane exceeds a firstthreshold; calculating a peak value of a magnitude of said accelerationdata projected onto said z-axis during said swing; and, determiningwhether said peak value of said magnitude of said acceleration dataprojected onto said z-axis exceeds a second threshold.
 7. The method ofclaim 1 further comprising: determining a time of start of downswing ofsaid swing; and, calculating a time to contact metric as a differencebetween said time of impact and said time of start of downswing.
 8. Themethod of claim 1 further comprising: calculating a trajectory of a handposition on said piece of equipment relative to said reference framebased on said sensor data.
 9. The method of claim 8 further comprising:calculating a center of rotation of said swing relative to saidreference frame based on said sensor data.
 10. The method of claim 9,wherein said calculating said center of rotation of said swing comprisescalculating said center of rotation as a point that is equidistant fromsaid hand position at three different points of said trajectory of saidhand position.
 11. The method of claim 10, further comprising:calculating an axis of rotation as an axis perpendicular to a planethrough said three different points of said trajectory of said handposition.
 12. The method of claim 11, wherein said one or more swingmetrics comprises a body tilt angle, wherein said body tilt anglecomprises an angle between said axis of rotation and a vertical axis.13. The method of claim 9 further comprising: calculating a two-levermodel of said swing based on said trajectory of said sweet spot; saidtrajectory of said hand position; said center of rotation; and, whereinsaid calculating said one or more swing metrics is based on saidtwo-lever model.
 14. The method of claim 13 wherein said two-lever modelcomprises a body lever extending from said center of rotation to saidhand position; and a bat lever extending from said hand position to saidsweet spot.
 15. The method of claim 14 wherein said one or more swingmetrics comprise a body ratio, wherein said body ratio comprises a ratioof a rotation of said body lever during said swing to a rotation of saidbat lever during said swing.
 16. The method of claim 14 wherein said oneor more swing metrics comprise a hinge angle based on a relativeorientation between said bat lever and said body lever, at one or morepoints in time during said swing.
 17. The method of claim 16 whereinsaid one or more swing metrics comprise a hinge angle at impact, whereinsaid hinge angle at impact comprises said hinge angle at said time ofimpact.
 18. The method of claim 16 wherein said one or more swingmetrics comprise a time of commit, wherein said time of commit is apoint in time wherein a rate of change of said hinge angle exceeds athreshold.
 19. The method of claim 18 wherein said one or more swingmetrics comprise a hinge angle at commit, wherein said hinge angle atcommit comprises said hinge angle at said time of commit.
 20. The methodof claim 16 wherein said one or more swing metrics comprise a hingeangle at impact, wherein said hinge angle at impact comprises said hingeangle at said time of impact; a time of commit, wherein said time ofcommit is a point in time wherein a rate of change of said hinge angleexceeds a threshold; a hinge angle at commit, wherein said hinge angleat commit comprises said hinge angle at said time of commit; and, ahinge release, wherein said hinge release comprises a difference betweensaid hinge angle at impact and said hinge angle at commit.
 21. Themethod of claim 1 further comprising determining a bat impact velocityvector as a velocity of said sweet spot at said time of impact; and,determining a swing plane as a plane through said sweet spot at saidtime of impact and spanned by said bat impact velocity vector and by alongitudinal axis of said piece of equipment at said time of impact. 22.The method of claim 21 further comprising calculating an off-planedistance as a distance between said sweet spot and said swing plane, atone or more points in time during said swing.
 23. The method of claim 22further comprising calculating a time on plane as an earliest time insaid swing when said off-plane distance is below a threshold and remainsbelow said threshold until said time of impact.
 24. The method of claim23 wherein said one or more swing metrics comprise an on-plane metric,wherein said on-plane metric comprises an angular range of motionbetween said time on plane and said time of impact.
 25. The method ofclaim 1 further comprising determining a forward bat velocity as avelocity of said sweet spot projected onto a plane perpendicular to alongitudinal axis of said bat, at one or more points in time during saidswing.
 26. The method of claim 25 wherein said one or more swing metricscomprise a bat speed, wherein said bat speed comprises a magnitude ofsaid forward bat velocity at said time of impact.
 27. The method ofclaim 26 wherein said one or more swing metrics comprise a swing power,wherein said swing power comprises a product of said bat speed, and amass of said piece of equipment, and an average acceleration of saidsweet spot during said swing.
 28. The method of claim 25 wherein saidone or more swing metrics comprise a peak bat speed, wherein said peakbat speed comprises a maximum magnitude of said forward bat velocityduring said swing.
 29. The method of claim 1 wherein said one or moreswing metrics comprise a swing plane tilt angle, wherein said swingplane tilt angle comprises an angle of a longitudinal axis of said pieceof equipment with respect to horizontal at said time of impact, or anattack angle, wherein said attack angle comprises an angle of a velocityvector of said sweet spot with respect to horizontal at said time ofimpact, or both said swing plane tilt angle and said attack angle. 30.The method of claim 1 further comprising: providing sound or image databased on said time series of sensor data, or providing metrics derivedfrom said time series of sensor data.